Pseudoreplication

[4] This definition omits the confounding of unit and treatment effects in a misspecified F-ratio.

For the effect of serial or temporal correlation also see Markov chain central limit theorem.

The problem of inadequate specification arises when treatments are assigned to units that are subsampled and the treatment F-ratio in an analysis of variance (ANOVA) table is formed with respect to the residual mean square rather than with respect to the among unit mean square.

The problem is eliminated by forming the F-ratio relative to the correct mean square in the ANOVA table (tank by treatment MS in the example above), where this is possible.

Replication increases the precision of an estimate, while randomization addresses the broader applicability of a sample to a population.

Pseudoreplication due to correlation of samples: without accounting for correlation the 90% confidence interval for the sample mean is much too small. To get around this problem for example the blocking method can be applied where correlated samples are first grouped, then the (for each block) the corresponding sample means are computed. From these two "block sample means" the total sample mean is computed as their average as well as the standard deviation. This gives a better estimate for the confidence interval of the sample mean. [ 5 ]